Truth function: Difference between revisions

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is false. In both cases, each component sentence (i.e. "''Al Gore was president of the USA on April 20, 2000''" and "''the moon is made of green cheese''") is false, but each compound sentence formed by prefixing the phrase "''Mary believes that''" differs in truth-value. That is, the truth-value of a sentence of the form "''Mary believes that...''" is not determined solely by the truth-value of its component sentence, and hence the (unary) [[Logical connective|connective]] (or simply ''operator'' since it is unary) is non-truth-functional.

The class of [[classical logic]] connectives (e.g. [[and (logic)|&]], [[material conditional|→]]) used in the construction of formulas is truth-functional. Their values for various truth-values as argument are usually given by [[truth table]]s. [[Truth-functional propositional calculus]] is a [[formal system]] wh10000whose formulae may be interpreted as either true or false.

e formulae may be interpreted as either true or false.

== Table of binary truth functions ==